A) 1 : 3
B) 1 : 9
C) 1 : 27
D) 9 : 1
E) 27 : 1
Correct Answer: C
Solution :
Excess of pressure inside a soap bubble \[p=\frac{4T}{R}\] or \[\frac{{{p}_{1}}}{{{p}_{2}}}=\frac{{{R}_{2}}}{{{R}_{1}}}\] Given \[{{p}_{1}}=3{{p}_{2}}\] \[\therefore \] \[\frac{3{{p}_{2}}}{{{p}_{2}}}=\frac{{{R}_{2}}}{{{R}_{1}}}\] or \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{1}{3}\] Therefore, ratio of volumes of bubbles \[\frac{{{V}_{1}}}{{{V}_{2}}}=\frac{\frac{4}{3}\pi {{R}_{1}}^{3}}{\frac{4}{3}\pi {{R}_{2}}^{3}}\] \[=\frac{{{R}_{1}}^{3}}{{{R}_{2}}^{3}}={{\left( \frac{1}{3} \right)}^{3}}=\frac{1}{27}\] \[\therefore \] \[{{V}_{1}}:{{V}_{2}}=1:27\]
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